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It does not guarantee that search engines will add all of your pages to their index or rank the pages very high. That depends on how valuable the search engines feels your pages are.
It is bad idea while placing 2000 links on a single page. You can use multiple sitemap pages and also create xml-sitemap and submit it to google.
I think you might be referring to html sitemaps that are intended to be used by humans. If you are creating a sitemap for your human visitors I would recommend to divide the links into smaller, more manageable pieces.
The original post seems to be asking about google sitemaps. Google sitemaps allows for a maximum of 10MB and a maximum of 50,000 URLs. If you do not want to upload a very large file for whatever reason, you can submit multiple, smaller sitemaps to Google.
Please remember that Google sitemaps are not intended for human use. It is intended to help googlebot to better crawl a website.